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harder 5x5 twin puzzles
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Posted on: Fri Jan 18, 2013 7:52 pm

Posts: 2281
Joined: Thu May 12, 2011 11:58 pm
harder 5x5 twin puzzles
Another one that has been "on the list" for a long time: the "difficult" 5x5 twins
of Wednesday and Thursday were too easy (usually perfectly possible to solve
them by themselves).

Starting this coming Wednesday, they should be quite a bit trickier (still doable
in a few minutes, but at least not trivial anymore).

Below is an example:

Posted on: Fri Jan 18, 2013 9:35 pm

Posts: 710
Joined: Fri May 13, 2011 6:51 pm
Re: harder 5x5 twin puzzles
pnm wrote:
Another one that has been "on the list" for a long time: the "difficult" 5x5 twins
of Wednesday and Thursday were too easy (usually perfectly possible to solve
them by themselves).

Starting this coming Wednesday, they should be quite a bit trickier (still doable
in a few minutes, but at least not trivial anymore).

Below is an example: ...

Interesting idea, Patrick, this is the way, it looks a little trickier, however in this particular case it is possible to solve the full twin puzzle using only the right puzzle, for instance (you can see it quickly), that is, the left puzzle is not providing information at all (in the past I talked in the Forum, IIRC in the thread "The essential info in a puzzle", about the difficulty of designning the twins so interleaved that it would be impossible to solve them without the cooperating info of both sides).

Posted on: Fri Jan 18, 2013 9:59 pm

Posts: 2281
Joined: Thu May 12, 2011 11:58 pm
Re: harder 5x5 twin puzzles
clm wrote:
Interesting idea, Patrick, this is the way, it looks a little trickier, however in this particular case it is possible to solve the full twin puzzle using only the right puzzle, for instance

Thanks for checking that, I'll raise the stakes a bit then

A slightly harder example (the left puzzle should not be solvable
on its own, for example):

Posted on: Fri Jan 18, 2013 11:36 pm

Posts: 710
Joined: Fri May 13, 2011 6:51 pm
Re: harder 5x5 twin puzzles
pnm wrote:
... I'll raise the stakes a bit then ...
A slightly harder example (the left puzzle should not be solvable
on its own, for example):
...

Yes, because the left puzzle by itself can have these two solutions (so not a unique solution):
21435
52314
34251
45123
13542

and

24153
32415
53241
15324
41532

but the right puzzle is solvable again alone (without the cooperation of the left side): c5 = 5 (addition rule, two leftmost columns) >>> c1 = 1, d1 = 5. Now, since: 9 + b2 + 6 + (15 - c3) = 30 (two upmost rows) >>> b2 = c3 and this quickly permits to eliminate a4 = 2, a5 = 1, b5 = 3 ... driving to the unique a4 = 1, a5 = 4, b5 = 1 >>> b1 = 4, a1 = 2 (e1 = 3), a2 = 3 >>> b2 = 2 = c3 ... finding inmediately the rest of the unique solution.

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